Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method
Stephan Wojtowytsch
math.AP, math.NA, stat.ML
Submitted: 2026-07-27
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- Optimal Learning
- Penalising the biases in norm regularisation enforces sparsity
- Neural network approximation and estimation of classifiers with classification boundary in a Barron class
- Weighted variation spaces and approximation by shallow ReLU networks
- A Priori Estimates of the Population Risk for Two-layer Neural Networks
- The Barron Space and the Flow-induced Function Spaces for Neural Network Models
- Some observations on high-dimensional partial differential equations with Barron data
- Group Equivariant Fourier Neural Operators for Partial Differential Equations
- Neural Operator: Learning Maps Between Function Spaces
- Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
- DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
- Fourier Neural Operator for Parametric Partial Differential Equations
- Complexity Measures for Neural Networks with General Activation Functions Using Path-based Norms
- Neural Scaling Laws of Deep ReLU and Deep Operator Network: A Theoretical Study
- A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case
- Approximation Rates for Neural Networks with General Activation Functions
- Characterization of the Variation Spaces Corresponding to Shallow Neural Networks
- Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks
- $L^p$ sampling numbers for the Fourier-analytic Barron space
- Solving the Poisson Equation with Dirichlet data by shallow ReLU$^\alpha$-networks: A regularity and approximation perspective
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